for the network.Hence, its quality has a large influence on the results of analyses based onthis trafficrepresentation. Mathematically, this estimation is called "under-estimated"because, in most of the cases, there are more unknown parameters (OD pairs flows) thaninformation

(traffic counts data)

to estimate those. Due to this point, OD estimation issolvedasan optimization problem. The methodology adopted must find the optimalsolution

depending on

the

modelling

constraints.

Toestimate

an OD matrix, several inputs are needed.The network model, traffic data (traffic counts at different places) and route choice algorithms(determination of the best paths in a network depending on trip and

the problem using static approaches. They are estimatinga unique OD matrix for the whole period study.

This limitation

does not allow fluctuations ofthe demand through time. In this way, dynamic characteristics of the demand, particularly inurban context, could not be obtained. Dynamic extension of the matrix based on traffic countcould be an alternative but adapts only the volume and not the structure of the demand.Sequential (time slided) static OD estimation is also proposed but this technique does

not takeinto account the continuity of the demand through the time (no link between different timeslides).

Demand variations

with

timeare

evaluated

in the case of dynamic OD estimation. To do that,the different stages of the OD estimation must be adapted to catch thisevolution. First, trafficassignment needs to be dynamic.

DTA (Dynamic Traffic Assignment) is going to propose aroute choice solution depending of traffic conditions. And, the OD adjustment, also, needs totake into account the evolution of trips in the network.Algorithm must be able tomake

adistinction between entrance time (in the network) and time period at the traffic countplace. Itneeds this information to takeinto account vehicles which use more than the time slice periodto go from entrance point to

traffic

countlocation.

In our case, we are going to focus on static and dynamic congested situations

years ago.The approach andmethodology are explained in detail butextensivetests are still in progress.

LITERATURE REVIEW

Static adjustment approach is the most common method for OD estimation.

In this

method,the inter-dependence between OD matrix and link flow is formulated as a bi-level problem

inmost of the cases (see Figure1)

[16].

Figure1

Bi-level process

For instance,the softwareEMME/2

(INRO), which is the most common used method forpractitioners

for static OD estimation,

assigns the traffic in the network (lower level) usingWardrop equilibrium

[25]

based on Volume Delay functions

defined

for eachlinkandjunction. These functions give the relationship between the travels time needed to cross thesection,

and flow on it.

Concerning

the upper level,Spiess has particularly worked on thefield of matrix adjustment and his paper

[21]

on Gradient approach could be considered as areference in this

domain. This paper presents a mathematical approach which formulates aconvex minimization problem using the direction of the steepest descent which could beapplied to large scale networks. With this process, the original OD matrix is not changed morethan necessary by following the direction of the steepest descent.

Spiessapproachis

dealing

with

the estimation of the OD flows in a static way. It means that theflow for each OD pairs is considered

as constant (no variation on volume) during the analyzedperiod. This hypothesis is very constrainedand does not

take

into account

on

the

evolutionofpeak hour

traffic(increaseand thendecrease of traffic demand

on

the network). Dynamicapproaches are indispensable toimprove the process accuracy.

The main contributions in thedynamic OD estimation fieldcould be categorized based on the methodology (seeTable 1). Thetype of network tested, the way to achieve the traffic assignment and the optimization approachfor the OD estimation form different groups.

developed a methodfor estimation OD flows on freeway networks in which time interval boundaries are determinedby analyzing time-spacetrajectories. Trajectories of the vehicles from the upstream end of thestudy section are computed and used to match measured link counts at various locations withcorrect set of OD flows. This new method is based on adopting a Truncated Multivariate Normal(TMVN) distribution for the split probabilities and updating this distribution using Bayes rule.

The method has been tested on the Amsterdam freeway network. This is a large beltway (32 km)which encircled

the city with 20 entrance and exit ramps. Routechoice is very limited (one wayor the other) and there is no signalized intersection.

The research by Cascetta

et al.

[7], Sherali

and Park

[20]

and Ashok

[1]

considered trafficassignment as an input

and

assignment is calculated analytically.

Ashok developed a sequentialOD smoothing scheme based on state-space modeling concept. Heused

a Kalman Filter solutionapproach to estimate the OD flows. He also discussed

about methods to estimate the initial inputsrequired by the Kalman filter algorithm.

The theoretical development is tested on three differentnetworks: the Massachusetts Turnpike, the I-880 near Hayward, California and AmsterdamBeltway. These networks are different in term of scale but with minimal or no route choice andno trafficsignal.

the LSQR presents better performance incomparison to the other approach.

The authors used

a very simple network for a numericalcomparison and two other networks as case studies. The first one is the Central Artery/ThirdHarbor Tunnel. It is a medium size network with low route choice possibilities, five origins andtwo destinations. Nodes are unsignalized. The secondnetwork

contains the major highways I-5,I-405, and CA-133 around Irvine, California.This is a medium scale network with 625 OD pairs(25*25 OD matrix), without signalized intersection. This network could also be considered closeto an urban network but even if the geographical size of the network is large, the complexity ofthe model (number of route possibilities) and the size of the matrix is medium.

Finally, urban networks are analyzed by fewresearchers. Traffic assignment could be known(input) or calculatedanalytically

a new method whichallows estimating the complex link between OD flows andtrafficcounts. The relationshipbetween flows and traffic measurements are captured using an optimization approach whichconsiders the assignment model as a black box. Assignment matrix and dynamic OD estimationare estimated mathematically. Two practical cases have been analyzed. The first

one is a smallnetwork constituted by four simple intersections (unsignalized) with three origins and onedestination (no route choice). The second one is named South Park, Los Angeles Network. It is amedium size network composedof

two

freeways and several arterial

roads. Most of the urban-

6

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intersections are signalized and route choice possibilities are medium.

provides a convergent, generalized iterative matrix scaling procedure for therecursive adjustment of the prior OD trip flows, RMART provides a diagonal search betweentwo successive iterations to improve its convergence speed and DIMAP is a suitablecombination of the aforementioned algorithms. Network tested is the greater Athens (44*44OD matrix) with interestingroute choice

possibilities and without traffic signal.

Many people have been interested in the field of OD estimationfor

numerous years. Thesedevelopment have followed mathematic and computers capabilities evolution. From the staticestimation on basic networks to complex algorithm on large networks, different approacheshave been explored.

WEAKNESS OF EXISTING

OD ESTIMATION METHODS

All approaches presented previously propose a solution to the OD estimation problem, butdisadvantages can be identified.

-

Static/Dynamic approach:

Disadvantagesor lacks of the static method can lead to outputs not adapted or incompatible foran exploitation of the data for detailed analyses. The static equilibrium does not allow a timedependant traffic variation adapted for dynamic flows modifications (essential

for short-termmicroscopic studies).

Moreover, depending of the complexity of the network (high number ofintersections), parameterization of Volume Delay functions is very difficult and seldom done indetail by practitioners.

Usually, to use a statically determined OD matrix in a dynamicsimulation (microsimulation with time dependant demand); it is common to modify thedemand based on traffic counts. The shape of traffic counts curves from main arterials is usedto reproduce the volume time variation of the demand. This method helps to represent theglobal variation in time but omit structure modifications of the matrix (commuter traffic ornon-uniform modifications changes on matrix values

for instance).

Another approach toevaluate variation of the demand in time is to do a sequential static OD estimation. The resultsare a matrix for each period of the time. This method could be considered as dynamic but itdoes not take into account previous time period in the calculation of

the actual one; there isnot link between different time periods. Using macroscopic simulator does not giveinformation about positions of vehicles in a section; therefore, it is impossible to getinformation about vehicles, which enter the network in a different time interval than the actualtraffic count. From these points, an integrated and global approach must be developed to takeinto accountdynamic variations of the demand.

-

Equilibrium research approach:

In the literature, we can find very little

consideration aboutcomplex

traffic route choice

possibilities

in the lower levelproblem(assignment matrix). It could be done by observation,

but we can see that the first one use a small and theoreticalnetwork (“much remains to be done to have a reliable dynamic OD system for efficient use in-

7

-

practice”)

and an

analytic approach for the assignment matrix

whereas the second one takes intoaccountonlyfreeways and main arterials.

Bierlaire

[5]

usesKalmanFiltering

in the Irvinenetwork. This network ismedium size

and offer route choice capabilities, without consideration

of traffic signals.In addition, this paper does not explain in detail how the assignment matrix isobtained andit is oriented on computing results

(efficiency)

more than matrix quality

(practicalapplication).

-

Urban applications:

As we can see in the

Table 1, there is very little consideration for urban network and for rarecases which are dealing with this kind of typography, usually they are small ones with lowroute choice and signalized capabilities. This lack could be problematic for most traffic

studies in city areas with congested and dense networks and signalized junctions. Majority ofthe traffic problematic are observed in urban area and present more challenging andinteresting task for traffic engineers. An innovative approach must allow efficient assessmentin various types of networks and not limited to specific cases.

Based on the deficiencies identified above, the proposed methodology is focusing on severalimprovements of the current solutions. First, the approach is formulated as a Bi-level problemand uses amesoscopic simulator

for demand assignment

which is

particularly adapted

for thelarge and complex urban networks. Quality of the equilibrium, route choice and level of detailof the network signals settings are important features to provide an assignment reallyrepresentative of the actual one for all traffic situations. Moreover, this assignment and alsothe OD matrix adjustment must be done dynamically. The proposed methodology is going totackle the major problems of the time dependant formulation e.g. travel time in the network,constraints on OD modification, negative flows, etc.

METHODOLOGY PROPOSED

To improve the demand modeling,this study

focuses

on the distribution of the traffic in thenetwork. This distribution has a strong influence on the utilization of the different roads

depending on origins and destinations

paths

and congestion level. The utilization of a simulationtool

can

allow an accurate and realistic modeling of the route choice in the road network.

In theupper level

problem, this repartition will be an input for OD matrix estimation algorithms.

Innovative approach(e.g.byaheuristic way using traffic simulation)

could be

applied

tosolve the lower level of the bi-level problem.Upper level will be solved using KalmanFiltering

(see Figure2).

-

8

-

Figure2

Detailed methodology proposed

Figure2

shows the details of the bi-level mechanism in the new approach.

Let’s see in moredetails the different parts of this

bi-level process.

Lower Level

problem

The aim

of the lower level is to assign the demand in the network,

to know how it influencestraffic counts

used in the upper level.

Using a simulator in the lower level allows

performingassignment on urban network and

extracting all the needed information useful for the process.Travel times, turn proportions,

shortest paths,flows, etc.

could be known for each places andfor each time

interval.

All type of

simulators could be use to assess the demand in the network. Macroscopic models

or forecasting models

use an aggregate user equilibrium approach and provide low detailinformation on vehicle (particularly in urban context due to discontinuous flows) and areusually static (constant demand in time). These characteristics do not match with ourobjectives.The other alternative isto use a fully disaggregated microsimulator for its dynamicand detailed capabilities. This kind of tool is adapted for detailed analysis of small networksbut is limited for large networks.

Indeed, calibration issues are dependent of the level of detailof the simulator and of the size of the network. Then, high number of calibration parameters(particularly the case for microsimulator) added to large networks lead to difficulties foraccurate calibration (moreover, this calibration is time consuming).From these statements,mesoscopic simulators which are situated between macrosimulator and microscopic modelsseem to be the most adapted tool. Mesoscopic simulator focuses on essential behavior withoutunnecessary details.

OD matrix is the important input of the system. This matrix must be asclose as possible to the researched one. Historical data (OD tables), observations (realtime…), surveys, investigations, determination of the mobility

attraction

poles are tools toevaluate the best initial OD matrix. First OD matrix from first OD estimation could also beobtained using gradient approach

([21])

and extended to a time sliced OD matrix usingobserved flows in main arterials.

Moreover, time dependenttraffic counts

are indispensablefor the matrix adjustment. This set of data is the only point which reflects the real trafficconditions in the network and represents the matching point of the process.



Mesoscopic simulation for dynamic user equilibrium

The aim of this step is to determine the assignment matrix which gives the different pathschoices depending on origin anddestination and traffic conditions. AIMSUN Mesoscopicsimulator is searching for Dynamic User Optimal (DUO) by iteration (see

[19]). Given thatthe network loading is based on a heuristic simulation approach, analytical proof ofconvergence to a user equilibrium cannot be provided, but empirically convergence to anequilibrium solution can be provided by the Rgap function, measuring the distance betweenthe current solution and an ideal equilibrium solution[11, 13]. A small value of Rgapexpresses equilibrium in the network close to the Dynamic User Optimal.

The simulator

isminimizing the Rgap value

usingMethod of Successive Averagestechnique

(MSA,[3]).

Where

are the travel times on the shortest paths for the i-th OD pair at time interval t,

is the travel time on path k connecting the i-th OD pair at time interval t,is theflow on path k at time t, gi(t) is the demand for the i-th OD pair at time interval t, Ki, is the setof paths for the i-th OD pair, and I isthe set of all OD pairs.

Using the AIMSUN Mesoscopic simulator allows accurate and realistic distribution of thetraffic in the network with short time for calibration. Its Rgap minimization using MSAprovides a dynamic user equilibrium indispensable forthe traffic assignment. Moreover,urban characteristics are fully modeled and route choose is as detailed as microscopicsimulation. As explained above, assignment of the traffic is particularly adapted for complexand large urban networks.

-

10

-

Upper level

problem

The proposed approach must find the best way to solve the upper levelproblemdepending on

inputs.Algorithms are going to try to minimize the gap between simulated data and observeddata by modification of the OD matrix used in the lower levelproblemto fit to thereal

values.

OD estimation could use existing method, of course adapted to the new constraints of the newapproach: Gradient, Least square,

Kalman Filtering, etc.



OD adjustment

To adjust the OD matrix dynamically,with

white and Gaussian errors

in the measurements andstate equations (

,

), and if these equations

are linear, KalmanFiltering

([14])propose theoptimal solution to the problem[15].

This process allows generating flow of the OD matrix atstate (t + 1) depending of the state (t) and an

assignment

matrix (which defines influences of ODflow on the different links). This approach takes into account dynamically the traffic evolution inthe network. The filter does an

estimation of a solution depending on a first "block"

(time slice)

of data and updates it using new data

(next time slice). Kalman filtering is defined

by twoequations which model the

evolution of the OD

flows

(solving as in[5]):

Transition Equation:

∑

Where

describes the effect of

on

and

is a random error.is the number of laggedOD flow assumed to affect

the OD flow in interval h+1.

Measurement Equation:

∑

Or

∑

Where

∑

is the fraction of the rth

OD flow that departed its origin during interval p and is on link lduring interval h.

is the measurement error.is the maximum number of time intervals takento travel between any OD pair of the network.

TEST NETWORKS

After the theoretical

approach, methodology has been coded as a plug-in of the AIMSUNsoftware.In

this way,dynamic OD estimation using mesosimulation and Kalman filtering isfully integrated in the package. Few parameters must be defined

as inputs

of the

process:

maximal number of iteration, minimumdifference

betweeniteration results fixe the criteria toleave the bi-level loop

are examples of criteria to exit the bi-level loop.

In a first step,reliability of the implementation of the new methodology must beassessed.

Very firstnetworks have been built

torun the plug-inpresented in the previous chapter. Thesenetworksaretheoretical

and basics

in term of

coding

but presentreal

route choice capabilities

and alltheneeded characteristics (trafficcounting values, route choice parameters…). The aim is tocheck theproperfunctioning of thedifferent steps of the methodology proposed. This partmainly focused onverification of the plug-in,good coherence and continuity betweendifferent stages of the process

(data transmission)

andaccuracy of the Kalman algorithmscalculation.

After this first step,

test network has been developed to testthe OD estimation

capabilities.

Beforeapplying

the methodology on a complex urban network, validation of the OD-

11

-

estimation

aspect on a "simple" case must be done. In this way, basic network withpathspossibilities

convergence, calibration parameters and queuing). In the upper level, estimation of ODcells based on Kalmanalgorithm is

followedduring

time periods and iterations.For this, thecity centre

of Lausanne city (Switzerland) will be use

for the next step (results presented in afurther paper).This is a 2.5

km x2.5

km (6.25

Km2) perimeter area representing a densenetwork where all the roads

and signals

have been considered. Congestion during eveningrush hours can be considered as moderate even if, some arterials are oversaturated

(particularly on the city centre exits and entrances). OD matrix size is 80*80.

Initial ODmatrices have been obtained using a static approach (common approach, see Chap."Literaturereview") and aboutthirty

traffic countsare going to be used to adjust the demand.

RESULTS

AND ISSUES

Following graphic

(Figure 3)

represents

the evolution of the demand (traffic flows) for severalOD pairs through iteration of the bi-level loop

for Dublin network (10*10 OD matrix, 100 ODpairs

and 15 counting stations). Initial demand has been obtained by multiplying theactualOD matrix by 0.8 (constant values for all cells). Adjustment of the flows by Kalman Filteringand stabilization to a feasible solution are observed

aftera fewiterations.

Figure3

OD pair flows through Iterations

-

12

-

The nextgraph

(Fig 4)

presents

the evolution of the relative difference between actual trafficcounts and simulated ones

in our case (urbanapplications).Complexity of the implementation for large networks and non-realistic solutions(negative flows) particularly forlow OD flows

are the most constrained limitations.

Fromthese lacks,it is important to evaluate an alternative tosolve

the Upper Level

problem.LSQRalgorithm presented in[6, 18]

is proposing a constraint solutionforthe same least squareproblemas the oneformulated for the KalmanFiltering. Non-negative bounds (and/or limitationin flows adjustment) could be apply and avoid inconsistent in results even for urban networkswith low OD pair flows. Moreover, an interesting asset of LSQR is its capability to deal withlarge matrices. Indeed, sizes ofthe LSQRmatrices are smaller due to the formulation of theproblem (and do not need to be stored) and resolution of the algorithm is simpler.

The proposed methodology is estimating dynamic OD matrices basedmainly on

trafficcounts. Therefore, a particular attention should be given to the quality ofinputs ofthe actualtraffic counts. Indeed, assignment matrixis obtained based on the set ofdetectors

(proportionsin each cell of the matrix are calculated at the positions of traffic counts). Then,

observedtraffic flows and this matrix

are used to adjust flows in the Upper level. A minimum number

of detectors

must beusedto be sure that at least each OD path is intercepted

by a countingstation. If not, KF could not propose flow adjustment because there is no information for

the

concerned

OD pair.

One particularity of the OD estimation problem is the under estimation. It means that theprocess is looking for a solution which satisfies the given conditions, but the number ofconditions is smaller than unknown values. In our case traffic counts and initial OD flows are-

13

-

the inputs. From these, a lot of different OD matrix can satisfy constraints defined by them.All those solutions are consistent with the problem. Therefore, it is difficult to discuss aboutthe absolute quality of theoutputs obtained.These results have to be evaluated in a relativeway. Robustness and consistency of the approach are important aspects of the evaluation andcanlead to favorable outcomes. Nevertheless, the proposed approach could be compared tothe static approach followed by the dynamic extension based on traffic counts (heuristics timeslicing of the static matrix, see Introduction).Dynamic quality of the outputs of differentapproaches will be tested and evaluated by microsimulations using actual networks. Severalnetworks and scenarios will be developedin this studyto test if the demand is representative,well defined and adapted for detailed study. Dynamic properties are going to be investigated byanalyzing the built up and distribution of congestion on the network during rush hours, thebehavior of the traffic in front of an accident, the creation of a traffic jam due to an accident andthe dissipation of the queue, creation, variation and evolution of length of queues, etc, comparedwith observed behavior.

It’s important to note that the different issues of the process are linked with the inputs used.The quality of the initial OD matrix (obtained by studies and investigations) could be verydifferent depending on the origin ofinformation. Data used to determine this matrix couldhave different structures or shapes. The dynamic matrix extension based on traffic countscould be more or less precise depending on this data quality.

In this way, a particular attentionmust be given also to this inputs and relative approach (using same initial OD matrices) aregoing to give results that are more realistic.

CONCLUSION

Traffic simulation is more and more widely used tool for planners

and managers

in the ITSarena.This tool allows scenario evaluation and

also online traffic assessment.Demandmodeling is one of the important inputs of simulators.In

this way,OD estimation is a crucialstep for any transportation studies. Demand quality influences strongly the results of detailedanalyses. Quality and quantity must be as close as possible to the real demand. Due to thecomplexity of the mathematical solving of this problem, OD estimation is an optimizationproblem whichhaves an infinite of solutions. The methodology adopted must find the optimalone depending on

the network constraints.

Thispaper presents a study

of existing methods andan innovative dynamic approach of theOD matrix determination process in urban area.The idea of using this dynamic process tofind the distribution of the traffic depending on the initial demand represents the advantage ofmeeting the needs of the next step, i.e. microsimulation studies. This approach is particularlyadapted to complex and dense urban network. Moreover, matrix adjustment is done usingKalman Filtering techniques to allow full consideration of dynamic particularities of urbannetworks.

Networks used are describedto highlight different parts

of the validation work ofthe developed plug-in. OD estimation consistency

and urban characteristicsare tested.Firstoutputs are presented and show interesting results. From them, limitations and issues fordynamic OD estimation using Kalman Filtering are identified.